Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $5 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot10^{4}\cdot20^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20I5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&110\\47&49\end{bmatrix}$, $\begin{bmatrix}53&40\\2&51\end{bmatrix}$, $\begin{bmatrix}79&40\\96&11\end{bmatrix}$, $\begin{bmatrix}99&10\\110&91\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.5.cmp.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $256$ |
| Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 20.144.1-20.i.1.1 | $20$ | $2$ | $2$ | $1$ | $0$ |
| 120.144.1-20.i.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.144.1-120.dh.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.144.1-120.dh.2.30 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.144.3-120.fse.2.18 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.fse.2.29 | $120$ | $2$ | $2$ | $3$ | $?$ |